Graduate Statistics Topic 5: Benchmark: Correlation and Regression Project

PSY-520 Graduate Statistics

Topic 5– Benchmark – Correlation and Regression Project

Directions: Use the following information to complete the questions below. While APA format is not required for the body of this assignment, solid academic writing is expected, and documentation of sources should be presented using APA formatting guidelines, which can be found in the APA Style Guide, located in the Student Success Center.

Player #	Players Age (x)	Batting Averages (y)	XY	X^2	Y^2
1	26	338	8788	676	14244
2	24	318	7632	576	101124
3	33	318	10494	1089	101124
4	33	316	10428	1089	99856
5	25	315	7875	625	99225
6	41	315	12915	1681	99225
7	24	312	7488	576	97344
8	29	307	8903	841	94249
9	34	304	10336	1156	92416
10	28	302	8428	784	91204
11	28	301	8428	784	90601
12	37	300	11100	1369	90000
13	34	289	10132	1156	88804
14	32	296	9472	1024	87616
15	39	295	11505	1521	87025
16	24	294	7056	576	86436
17	24	294	7056	576	8646
18	30	293	8790	900	85849
19	38	289	10982	1444	83521
20	34	288	9792	1156	82944
21	36	287	10332	1296	82369
22	32	287	9184	1024	82369
23	33	286	9438	1089	81796
24	31	285	8835	961	81225
25	28	284	7952	784	80656
26	31	284	8804	961	80656
27	29	278	8062	841	77284
28	26	276	7126	676	76176
29	29	275	7975	841	75625
30	22	274	6028	484	75076
31	24	274	6576	576	75076
32	31	273	8463	961	74529
33	23	271	6233	529	73441
34	29	271	7859	841	73441
35	26	270	7020	676	72900
36	29	268	7772	841	71824
37	37	268	9916	1369	71824
38	26	267	6942	676	71289
39	25	267	6675	625	71289
R=.06	∑x=1164	∑y=11338	∑xy=338870	∑x^2=34082	∑y^2=3208088

Model	B	Std Error	Standardized Coefficients Beta	t	Sig
1 Constant	275.146	17.817		15.443	.000
Age	.522	.589	.144	.885	.382

-The R-value of the linear model represents a correlation of 0.144. This is a low correlation. R square represents the variation of the DV, batting averages. This is a weak correlation of 0.6%.

Select at least three variables that you believe have a linear relationship.
- Specify which variable is dependent and which are independent.
- Independent variable: MLB baseball player’s ages
- Dependent variable: Batting averages in 2016
- 3rd variable: Player # used to chronologically order players to help eliminate outliers
Collect the data for these variables and describe your data collection technique and why it was appropriate as well as why the sample size was best.
-Data was collected through a website that listed the top 2016 MLB baseball players by age and batting average. There were 39 players total which reflected the total top batters in 2016 aside from the total MLB baseball player population.
- Submit the data collected by submitting the SPSS data file with your submission.
- Frequency Table:
Find the Correlation coefficient for each of the possible pairings of dependent and independent variables and describe the relationship in terms of strength and direction.
-The constant is the batting average (y). The sig for the DV is 0, and the ID, age is 382 which is Pearson’ correlation coefficient (r). A sig with a small value between 0 and 1, the greater chance the correlation sign similar would be observed.
Coefficients
Unstandardized Coefficients
Find a linear model of the relationship between the three (or more) variables of interest.

Model SummaryModelRR square Adjusted r square Std Error of the estimate 1.873^2.762.749874.779

-A linear correlation is best represented with a regression line (straight). Based upon the data collected, the relationship between ages of MLB players and batting averages is positive, although weak. There is no statistical significance of a strong correlation in the questioned relationship.